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Question
The length of the diagonals of a rhombus is in ratio 4 : 3. If its area is 384 cm2, find its side.
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Solution
Let the lengths of the diagonals of a rhombus are 4x, 3x.
∴ Area of the rhombus = `1/2 xx ("Product of its diagonals")`
= `1/2 (4x xx 3x) = 384` (given)
⇒ `6x^2 = 384 ⇒ x^2 = 64`
⇒ x = 8 cm
∴ Diagonals are `4 xx 8 = 32` cm and `3(8) = 24` cm.
∴ OC = 16 cm and OD = 12 cm
∴ Side DC = `sqrt("OC"^2 + "OD"^2)`
∴ Side DC = `sqrt(16^2 + 12^2)` [By Pythagoras Theorem in ΔDOC]
= `sqrt(256 + 144) = sqrt(400) = 20` cm
Hence , side of the rhombus = 20 cm.
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